Search results

In [[astrophysics]], '''Chandrasekhar's variational principle''' provides the stability criterion for a static [[barotropic]] [ <ref>Chandrasekhar, S. "A general variational principle governing the radial and the non-radial oscillations of gaseous m ...

{{about|the book by [[Ramamurti Shankar]]|the book by [[Paul Dirac]]|The Principles of Quantum Mechanics}} | name = Principles of Quantum Mechanics ...

...]s, the Clebsch representation leads to a rotational-flow form of [[Luke's variational principle]].<ref>{{harvtxt|Luke|1967}}</ref> ...s in the two-dimensional motion of a compressible fluid and the associated variational problems | volume=125 | issue=799 | pages=598–618 | year=1929 | doi=10.1098 ...

...tional of <math>g</math>. The Bogoliubov causality condition in terms of [[variational derivative]]s has the form: ...N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov (1990): ''General Principles of Quantum Field Theory''. Kluwer Academic Publishers, Dordrecht [Holland]; ...

...</ref> This article shows how '''Newell's method''' fits in the context of variational theory. == Basic principles of variational theory (VT) == ...

==Variational principles == In particular symplectic and variational integrators are proving particularly accurate for long-term integration of ...

...=Kingshuk | last3=Lee | first3=Julian | last4=Dill | first4=Ken A. | title=Principles of maximum entropy and maximum caliber in statistical physics | journal=Rev ...4=Dill | first4=Ken A. | title=Communication: Maximum caliber is a general variational principle for nonequilibrium statistical mechanics | journal=The Journal of ...

In [[mathematical analysis]], '''Ekeland's variational principle''', discovered by [[Ivar Ekeland]],<ref name="Eke74">{{cite journ ...last2=Temam|first2=Roger|author2link=Roger Temam|title=Convex analysis and variational problems|edition=Corrected reprinting of the (1976) North-Holland|series=Cl ...

satisfy a variational principle, that is to say they minimize the functional == Connection with variational inequalities == ...

Standard [[variational method|variational procedure]] according to [[Hamilton's principle]] is applied to action which is integral of energy. Stationary action is conditional upon zero variational derivatives {{math|''δS''/''δx''^λ}} and leads to [[Euler–Lagrang ...

...ries]] by [[Padé approximant]]s. It is also closely related to [[Schwinger variational principle]]. ...first iteration of MCFV method we get the same result as from [[Schwinger variational principle]] with trial function <math> |\psi\rangle = |\phi\rangle</math>. ...

...JChEd..88.1521S |issn=0021-9584}}</ref> The basis for this method is the [[variational principle]].<ref name=Griffiths1995>{{cite book |last=Griffiths |first=D. J ...], [[density matrix renormalization group]], and [[Ritz method]] apply the variational method. ...

...''' is a [[Lagrangian (field theory)|Lagrangian]] [[Calculus of variations|variational]] description of the motion of [[ocean surface wave|surface waves]] on a [[ | title = A Variational Principle for a Fluid with a Free Surface ...

...blem''' is a classic motivating example in the [[mathematical]] study of [[variational inequalities]] and [[free boundary problem]]s. The problem is to find the [ ...dell'ostacolo''.<ref>"Some time after Stampacchia, starting again from his variational inequality, opened a new field of research, which revealed itself as import ...

| title = Tensors, Differential Forms, and Variational Principles ...

{{Short description|Fundamental mechanical principles}} ...two states of the system is called the [[action (physics)|action]]. Action principles apply the [[calculus of variation]] to the action. The action depends on th ...

...rally identical to the [[Einstein field equations]] are derivable from a [[variational principle]]. A [[spin tensor]] can also be supported in a manner similar t ...s of fields not affect the physical content of the field equations. These principles lead to the introduction of a new pair of linear functions, the position-ga ...

...mplitude]], [[frequency]] and [[wavenumber]]). By [[Noether's theorem]], [[variational principle|variation]] of the averaged Lagrangian <math>\mathcal{L}</math> w ===Variational formulation=== ...

...nglish, and other languages. Ekeland is known as the author of [[Ekeland's variational principle]] and for his use of the [[Shapley–Folkman lemma]] in [[optimizat Ekeland has contributed to [[mathematical analysis]], particularly to [[variational calculus]] and [[mathematical optimization]]. ...

...lem with complicated computational regions. The PDE is first recast into a variational form which essentially forces the mean error to be small everywhere. The di # Finlayson, B. A., 1972. The Method of Weighed Residuals and Variational Principles. Academic Press. ...